(VAR IL L M N V V1 V2 X X1 X2 X3 X4 )
(RULES 
        a__zeros -> cons(0, zeros)
        a__U11(tt, L) -> s(a__length(mark(L)))
        a__U21(tt) -> nil
        a__U31(tt, IL, M, N) -> cons(mark(N), take(M, IL))
        a__and(tt, X) -> mark(X)
        a__isNat(0) -> tt
        a__isNat(length(V1)) -> a__isNatList(V1)
        a__isNat(s(V1)) -> a__isNat(V1)
        a__isNatIList(V) -> a__isNatList(V)
        a__isNatIList(zeros) -> tt
        a__isNatIList(cons(V1, V2)) -> a__and(a__isNat(V1), isNatIList(V2))
        a__isNatList(nil) -> tt
        a__isNatList(cons(V1, V2)) -> a__and(a__isNat(V1), isNatList(V2))
        a__isNatList(take(V1, V2)) -> a__and(a__isNat(V1), isNatIList(V2))
        a__length(nil) -> 0
        a__length(cons(N, L)) -> a__U11(a__and(a__isNatList(L), isNat(N)), L)
        a__take(0, IL) -> a__U21(a__isNatIList(IL))
        a__take(s(M), cons(N, IL)) -> a__U31(a__and(a__isNatIList(IL), and(isNat(M), isNat(N))), IL, M, N)
        mark(zeros) -> a__zeros
        mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
        mark(length(X)) -> a__length(mark(X))
        mark(U21(X)) -> a__U21(mark(X))
        mark(U31(X1, X2, X3, X4)) -> a__U31(mark(X1), X2, X3, X4)
        mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
        mark(and(X1, X2)) -> a__and(mark(X1), X2)
        mark(isNat(X)) -> a__isNat(X)
        mark(isNatList(X)) -> a__isNatList(X)
        mark(isNatIList(X)) -> a__isNatIList(X)
        mark(cons(X1, X2)) -> cons(mark(X1), X2)
        mark(0) -> 0
        mark(tt) -> tt
        mark(s(X)) -> s(mark(X))
        mark(nil) -> nil
        a__zeros -> zeros
        a__U11(X1, X2) -> U11(X1, X2)
        a__length(X) -> length(X)
        a__U21(X) -> U21(X)
        a__U31(X1, X2, X3, X4) -> U31(X1, X2, X3, X4)
        a__take(X1, X2) -> take(X1, X2)
        a__and(X1, X2) -> and(X1, X2)
        a__isNat(X) -> isNat(X)
        a__isNatList(X) -> isNatList(X)
        a__isNatIList(X) -> isNatIList(X)
        
)